KAMPALA, Uganda—The deadly Ebola outbreak that has been raging in the Democratic Republic of Congo for more than 10 months has crossed into neighboring Uganda, where authorities on Tuesday said a 5-year-old boy tested positive for the hemorrhagic fever.

The spread of the disease across the border is a major setback for local and international health officials who have failed to contain the Ebola outbreak in Congo’s Ituri and North Kivu provinces, the world’s first in an active conflict zone. The World Health Organization and...